Question

❌ NO SPAMS PLEASE ❌ Integrate with respect to x. ​

Answer 1

Answer:

x^³/x^²+4x^²/1+5x/6x-1

x+4x^²+5/2-1

x+4x^²+3/2

Answer 2

Here Is your Answer

I would like to write numerator in terms of denominator

• Numerator......

x³- 4x² + 5x - 1

x³ - ( 4x² - 5x + 1 )

x³ - (4x-1)(x-1)

• Denominator = (x-1)²

Given integral

x³/(x-1)²- (4x-1)(x-1)/(x-1)²

x³.dx/(x-1)² - (4x-1).dx/(x-1)

Integration Of First term

Let 1/(x-1) = y

Given Integral turns....

-x³.dy.....(1)

1/(x-1) = y

1/y = x-1

X = 1/y + 1....Put in (1)

-(1/y + 1)³.dy

-(1/y³ + 1 +3/y² + 3/y)dy

-( -1/2y² + y - 3/y + 3lny )..... Integration of 1st term

put the value of y in term of X to get the whole in term of X....

Integration of Second term

-(4x-1)/(x-1)

Add and subtract 3 in numerator

-(4x-4 +3)/(x-1)

-4(x-1)/(x-1) - 3/(x-1)

-4 - 3/(x-1)

-4x - 3ln(x-1)..... Integration of second term

Now add both to get the answer

Miss u